Clustering based polyhedral conic  functions algorithm in classification

Gurkan Ozturk; Mehmet Tahir Ciftci

doi:10.3934/jimo.2015.11.921

Article Contents

2015, Volume 11, Issue 3: 921-932. Doi: 10.3934/jimo.2015.11.921

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Clustering based polyhedral conic functions algorithm in classification

Gurkan Ozturk^1, and
Mehmet Tahir Ciftci^2,

1.
Department of Industrial Engineering, Faculty of Engineering, Anadolu University, Eskisehir, 26555
2.
Vitra, Eczacibasi Yapi Gerecleri, 11300 Bilecik

Received: September 30, 2013

Revised: May 31, 2014

Published: June 2015

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Abstract

In this study, a new algorithm based on polyhedral conic functions (PCFs) is developed to solve multi-class supervised data classification problems. The $k$ PCFs are constructed for each class in order to separate it from the rest of the data set. The $k$-means algorithm is applied to find vertices of PCFs and then a linear programming model is solved to calculate the parameters of each PCF. The separating functions for each class are obtained as a pointwise minimum of the PCFs. A class label is assigned to the test point according to its minimum value over all separating functions. In order to demonstrate the performance of the proposed algorithm, it is applied to solve classification problems in publicly available data sets. The comparative results with some mainstream classifiers are presented.

Keywords:

Mathematics Subject Classification: Primary: 68Q32, 46N10; Secondary: 97R50.

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